Methods and systems for anonymously tracking and/or analysing individuals based on biometric data

ABSTRACT

Methods and systems are provided for anonymously tracking and/or analyzing flow or movement of individual subjects and/or objects using biometric data. A computer-implemented method enabling anonymous estimation of the amount and/or flow of individual subjects and/or objects, referred to as individuals, in a population moving and/or coinciding between two or more subject states using biometric data includes receiving identifying data, wherein the identifying data includes and/or is based on biometric data, from two or more individuals; generating, online and by one or more processors, an anonymized identifier for each individual; and storing: the anonymized identifier of each individual together with data representing a subject state; and/or a skew measure of such an anonymized identifier.

TECHNICAL FIELD

The invention generally relates to the issue of anonymity in technological applications; and technological aspects of data collection and data/population statistics based on biometric data, and more specifically concerns the technical field of estimating or measuring population flows and/or methods and systems and computer programs for enabling such estimation of population flows based on biometric data.

BACKGROUND

Legislation and public opinion increasingly drive a movement towards a right of anonymity in technology. This stands in conflicts with a need to collect data about population flows in order to automate or optimize processes and societies.

Retailers would like to collect statistics on their visitors in order to improve their operation. Smart cities are in need of data for optimizing the living quality and energy efficiency. Public transport systems need to collect data on travel patterns in order to reduce travel times and optimize costs.

Technologies that enable both data collection for statistical purposes while preserving personal anonymity is in high demand. In particular the tracking of flows of people from one point and time to another are problematic, since the reidentification of an individual at a later time is commonly the very definition of a breach of said individuals right to anonymity. This means that the whole idea of anonymous tracking of a population is somewhat counter-intuitive, since it is often practically impossible on the individual level.

Current privacy-enhancing methodologies used for tracking people that are based on pseudo-anonymization and unique identifiers are clearly unable to fulfill these needs, which means that companies avoid collecting data on population flows at all. It is highly desirable to find any systems able to collect data on such population flows without violating anonymity. In particular, profiling is widely considered to threaten the fundamental rights and freedoms of individuals. In some cases, encryption with a very minor destruction of information has been used, so that individuals can be reidentified with sufficiently high probability (commonly with error rates of one in several tens of thousands of identifications) that any misidentification can be neglected altogether. However, such pseudonymization techniques, irrespective of whether they are or are not practically reversible, are not deemed to be compatible with the legislative interpretation of anonymization nor with public opinion of the same, since the possibility of the reidentification act itself is a defining attribute of personal data.

SUMMARY

It is a general object to provide a system for providing anonymity while calculating statistics on populations based on biometric data.

It is a specific object to provide a system and method for preserving anonymity while estimating or measuring the flow of individuals, based on biometric data, between two or more tempo-spatial locations, computer system states in an interaction with the user and/or states of the health and health monitoring of a subject (collectively or individually referred to as subject states).

It is another object to provide a system for anonymously tracking and/or analysing transition and/or flow and/or movement of individual subjects and/or objects, referred to as individuals, based on biometric data.

It is also an object to provide a surveillance system comprising such a system.

Yet another object is to provide a computer-implemented method for enabling estimation of the amount or number of individuals in a population coinciding between two or more subject states based on biometric data.

A further object is to provide a method for generating a measure of flow or movement of individual subjects and/or objects, referred to as individuals, between subject states based on biometric data.

Still another object is to provide a computer program and/or computer-program product configured to perform such a computer-implemented method.

These and other objects are met by embodiments as defined herein.

According to a first aspect, there is provided a system comprising:

-   -   one or more processors;     -   an anonymization module configured to, by the one or more         processors: receive, for each one of a multitude of individuals         comprising individual subjects and/or objects in a population of         individuals, identifying information representative of an         identity of the individual, wherein the identifying information         representative of the identity of the individual includes and/or         is based on biometric data, and to generate anonymous identifier         skew measures based on identifying information of one or more         individuals;     -   a memory configured to store at least one anonymous identifier         skew measure based on at least one of the generated identifier         skew measures;     -   an estimator configured to, by the one or more processors:         receive, from said memory and/or directly from said         anonymization module, a number of anonymous identifier skew         measures, at least one identifier skew measure for each of at         least two subject states of individuals, and to generate one or         more population flow measures related to individuals passing         from one subject state to another subject state based on the         received anonymous identifier skew measures.

According to a second aspect, there is provided a system for anonymously tracking and/or analysing flow or movement of individual subjects and/or objects, referred to as individuals, between subject states based on biometric data.

The system is configured to determine, for each individual in a population of multiple individuals, an anonymized identifier using identifying information representative of an identity of the individual as input, wherein the identifying information representative of the identity of the individual includes and/or is based on biometric data. Each anonymized identifier corresponds to any individual in a group of individuals, the identity information of which results in the same anonymized identifier with probabilities such that no individual generates the anonymized identifier with greater probability than the sum of the probabilities of generating the identifier over all other individuals.

The system is further configured to keep track of skew measures, one skew measure for each of two or more subject states, wherein each skew measure is generated based on anonymized identifiers associated with the corresponding individuals associated with a specific corresponding subject state.

The system is also configured to determine at least one population flow measure representative of the number of individuals passing from a first subject state to a second subject state based on the skew measures corresponding to the subject states.

According to a third aspect, there is provided a surveillance system comprising a system according to the first or second aspect.

According to a fourth aspect, there is provided a computer-implemented method for enabling anonymous estimation of the amount and/or flow of individual subjects and/or objects, referred to as individuals, in a population moving and/or coinciding between two or more subject states, based on biometric data. The method comprises the steps of:

-   -   receiving identifying data from two or more individuals, wherein         the identifying data of each individual includes and/or is based         on biometric data;     -   generating, online and by one or more processors, an anonymized         identifier for each individual; and     -   storing: the anonymized identifier of each individual together         with data representing a subject state; and/or a skew measure of         such an anonymized identifier.

According to a fifth aspect, there is provided a computer-implemented method for generating a measure of flow or movement of individual subjects and/or objects, referred to as individuals, between subject states, based on biometric data. The method comprises the steps of:

-   -   configuring one or more processors to receive anonymous         identifier skew measures generated based on biometrically based         identifiers from visits and/or occurrences of individuals to         and/or in each of two subject states, wherein each identifier is         representative of the identity of an individual and includes         and/or is based on biometric data;     -   generating, using said one or more processors, a population flow         measure between two subject states by comparing the anonymous         identifier skew measures between the subject states;     -   storing said population flow measure to a memory.

According to a sixth aspect, there is provided a computer program comprising instructions, which when executed by at least one processor, cause the at least one processor to perform the computer-implemented method according to the fourth aspect and/or fifth aspect.

According to a seventh aspect, there is provided a computer-program product comprising a non-transitory computer-readable medium having stored thereon such a computer program.

According to an eight aspect, there is provided a system for performing the method according to the fourth aspect and/or fifth aspect.

In this way, it is actually possible to provide anonymity while allowing data collection and calculation of statistics on populations of individuals based on biometric data.

In particular, the proposed technology enables preservation of anonymity while estimating or measuring the flow of individuals between two or more subject states based on biometric data.

In particular, the proposed invention allows linking data points collected at different times based on biometric data for statistical purposes without storing personal data.

In general, the invention provides improved technologies for enabling and/or securing anonymity in connection with data collection and statistics based on biometric data.

Other advantages offered by the invention will be appreciated when reading the below description of embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention, together with further objects and advantages thereof, may best be understood by making reference to the following description taken together with the accompanying drawings, in which:

FIG. 1A is a schematic diagram illustrating an example of a system according to an embodiment.

FIG. 1B is a schematic flow diagram illustrating an example of a computer-implemented method for enabling anonymous estimation of the amount and/or flow of individual subjects and/or objects, referred to as individuals, in a population moving and/or coinciding between two or more subject states.

FIG. 1C is a schematic flow diagram illustrating another extended example of a computer-implemented method for enabling anonymous estimation of the amount and/or flow of individual subjects and/or objects.

FIG. 1D is a schematic flow diagram illustrating an example of a computer-implemented method for generating a measure of flow or movement of individual subjects and/or objects, referred to as individuals, between subject states.

FIG. 2 is a schematic diagram illustrating an example of micro-aggregation of a population into groups.

FIG. 3 is a schematic diagram illustrating another example of micro-aggregation of a population into groups, including the concept of skew measures.

FIG. 4 is a schematic diagram illustrating how each group of individuals may be associated with a set of subject states N, each for a set of points in time.

FIG. 5 is a schematic diagram illustrating examples of subject states such as tempo-spatial location data and useful identifying biometric information (ID).

FIG. 6 is a schematic diagram illustrating an example of a surveillance system.

FIG. 7 is a schematic flow diagram illustrating an example of a computer-implemented method for enabling estimation of the amount or number of individuals in a population coinciding between two or more tempo-spatial locations.

FIG. 8 is a schematic flow diagram illustrating another example of a computer-implemented method for enabling estimation of the amount or number of individuals in a population coinciding between two or more tempo-spatial locations.

FIG. 9 is a schematic diagram illustrating an example of movement or flow of one or more individuals from location A to location B.

FIG. 10 is a schematic diagram illustrating an example of movement or flow of users from one virtual location such as an IP location to another virtual location.

FIG. 11 is a schematic diagram illustrating an example of a computer-implementation according to an embodiment.

FIG. 12 is a schematic flow diagram illustrating an example of a computer-implemented method for generating a measure of flow or movement of individual subjects and/or objects, referred to as individuals, between tempo-spatial locations.

FIG. 13 is a schematic diagram illustrating an example of how an identifier skew measure can be made anonymous by adding noise at one or more times and how this can generate a bias compensation term.

FIG. 14 is illustrating an example of noise-masking anonymization.

DETAILED DESCRIPTION

Throughout the drawings, the same reference numbers are used for similar or corresponding elements.

For a better understanding of the proposed technology, it may be useful to begin with a brief analysis of the technical problem.

A careful analysis by the inventor has revealed that it is possible to anonymize personal data by storing a partial identity, i.e. partial information about the identity of a person that is not in itself personal data. Further, it is, perhaps surprisingly, possible to construct a system that is able to measure population flows using such anonymous data even in case this anonymous data is based on factors that are not directly related to the population flows and/or their distribution. Importantly, the proposed invention also works if the used factors are uncorrelated with the population flows and/or if any estimation of their a priori distribution would be infeasible. The invention is thus applicable on general populations using almost any identifying factors (i.e. types of data) without any need for further knowledge of the underlying distributions.

The invention offers systems and methods for estimating the population flow anonymously. Also provided are three specific anonymization methods and systems suitable for enabling these purposes. In brief, two such anonymization methods, hashing and noise-masking, are based on anonymizing identifying information concerning each visits to subject states in an anonymization module, while the third method is based on anonymizing the required stored data, i.e. the identifier skew measure. These methods can also be used in combination with each other.

The invention also provides a way for using the invention without first estimating the underlying distribution through the use of a decorrelating hashing module and/or a decorrelation module and/or a decorrelating skew measure.

In the following non-limiting examples of the proposed technology will be described, with reference to the exemplary schematic diagrams of FIG. 1 to FIG. 11.

FIG. 1A is a schematic diagram illustrating an example of a system according to an embodiment. In this particular example, the system 10 basically comprises one or more processors 11, an anonymization module 12, an estimator 13, an input/output module 14, and a memory 15 with one or more skew measures 16

According to a first aspect of the invention, there is provided a system 10 comprising:

-   -   one or more processors 11; 110;     -   an anonymization module 12 configured to, by the one or more         processors 11; 110: receive, for each one of a multitude of         individuals comprising individual subjects and/or objects in a         population of individuals, identifying information         representative of an identity of the individual, wherein the         identifying information representative of the identity of the         individual includes and/or is based on biometric data, and to         generate anonymous identifier skew measures based on identifying         information of one or more individuals;     -   a memory 15; 120 configured to store at least one anonymous         identifier skew measure based on at least one of the generated         identifier skew measures;     -   an estimator 13 configured to, by the one or more processors 11;         110: receive, from said memory and/or directly from said         anonymization module, a number of anonymous identifier skew         measures, at least one identifier skew measure for each of at         least two subject states of individuals, and to generate one or         more population flow measures related to individuals passing         from one subject state to another subject state based on the         received anonymous identifier skew measures.

By way of example, each identifier skew measure is generated based on two or more identifier density estimates and/or one or more values generated based on identifier density estimates.

For example, each identifier skew measure is representing the skew of the identifying information of one or more individuals compared to the expected distribution of such identifying information in the population.

In a particular example, the identifier skew measure of the anonymization module is based on a group identifier representing a multitude of individuals.

For example, the identifier skew measure may be based on a visitation counter.

By way of example, the identifier skew measure is generated based on the identifying information using a hashing function.

For example, the anonymization module 12 may be configured to generate a group identifier based on the biometric information of the individual by using a locality-sensitive hashing (LSH) function.

As an example, said one or more population flow measures includes the number and/or ratio of visitors passing from one tempo-spatial location/locality to another tempo-spatial location/locality.

For example, at least one of said one or more population flow measures is generated at least partly based on a linear transform of counter information of two or more visitation counters.

Optionally, the anonymization module 12 and/or the identifying information representative of the identity of an individual is stochastic and wherein the stochasticity of the identifying information and/or anonymization module 12 is taken into consideration when generating the linear transform.

For example, a baseline corresponding to the expected correlation from two independently generated populations is subtracted when generating the population flow measure(s).

By way of example, each identifier skew measure may be generated using a combination of the identifier and noise such that the contribution to the identifier skew measure is rendered anonymous due to a sufficient noise level for a visit to a subject state not being attributable to a specific identifier.

As an example, the identifier skew measure may be based on two or more identifier density estimates.

In a particular example, the anonymization module is configured to generate at least one identifier skew measure based on the anonymous identifier skew measure(s) stored in memory; and anonymity is provided by having added sufficient noise to the anonymous identifier skew measure stored in memory, at one or more moments, for the total contribution from any single identifier to be undeterminable.

Optionally, information about the generated noise sample(s) are also stored and used for the lowering the variance in the population flow measure.

By way of example, the identifying information representative of the identity of an individual may include and/or be based on at least one of the following non-limiting examples of biometric data: iris images, facial images, feature vectors, body images, fingerprint and/or gait.

In other words, the identifying information may be regarded as biometric information representative of an identity of the individual.

By way of example, the subject states include tempo-spatial locations, computer system states in an interaction with the user and/or states of the health and health monitoring of a subject.

By way of example, a biometric feature vector is based on a neural network extracting a representation likely to represent biometric data from an image containing biometric information.

By way of example, the identifying data might also contain, encode and/or represent additional identifying data in addition to the biometric data, for example image data or feature vectors based on image data also containing clothing and/or other non-biometric data together with for example a face.

In a particular example, which will be elaborated on in further detail later on, the subject states are tempo-spatial locations and/or localities, and

-   -   the anonymization module 12 is configured to generate a group         identifier based on the identifying information of the         individual to effectively perform microaggregation of the         population into corresponding groups;     -   the memory 15; 120 is configured to store visitation counters         for each of two or more group identifiers from each of two or         more tempo-spatial locations or localities associated with the         corresponding individuals; and     -   the estimator 13 is configured to receive counter information         from at least two visitation counters, and generate one or more         population flow measures related to individuals passing from one         tempo-spatial location to another tempo-spatial location.

For example, the anonymization module may be configured to generate a group identifier based on the identifying information of the individual by using a hashing function.

By way of example, the system 10; 100 comprises an input module 14; 140 configured to, by the one or more processors 11; 110: receive location data, for each one of the multitude of individuals, representative of a tempo-spatial location, and match the tempo-spatial location of the individual with a visitation counter corresponding to the group identifier related to the individual, and each visitation counter for each group identifier also corresponds to a specific tempo-spatial location.

According to a second aspect, there is provided a system 10; 100 for anonymously tracking and/or analysing flow or movement of individual subjects and/or objects, referred to as individuals, between subject states, based on biometric data.

The system 10; 100 is configured to determine, for each individual in a population of multiple individuals, an anonymized identifier using identifying information representative of an identity of the individual as input, wherein the identifying information representative of the identity of the individual includes and/or is based on biometric data. Each anonymized identifier corresponds to any individual in a group of individuals, the identity information of which results in the same anonymized identifier with probabilities such that no individual generates the anonymized identifier with greater probability than the sum of the probabilities of generating the identifier over all other individuals.

The system 10; 100 is configured to keep track of skew measures, one skew measure for each of two or more subject states, wherein each skew measure is generated based on anonymized identifiers associated with the corresponding individuals associated with a specific corresponding subject state.

The system 10; 100 is also configured to determine at least one population flow measure representative of the number of individuals passing from a first subject state to a second subject state based on the skew measures corresponding to the subject states.

By way of example, the anonymized identifiers are group identifiers and/or noise-masked identifiers.

In a particular, non-limiting example, the system 10; 100 is configured to determine, for each individual in a population of multiple individuals, a group identifier based on a hashing function using information representative of an identity of the individual as input.

Each group identifier corresponds to a group of individuals, the identity information of which results in the same group identifier, thereby effectively performing microaggregation of the population into at least two groups.

In this example, the subject states are tempo-spatial locations or localities and the skew measures correspond to visitation data, and the system 10; 100 is configured to keep track, per group, of visitation data representing the number of visits to two or more tempo-spatial locations by individuals belonging to the group.

The system 10; 100 is further configured to determine at least one population flow measure representative of the number of individuals passing from a first tempo-spatial location to a second tempo-spatial location based on visitation data per group identifier.

For example, the system 10; 100 comprises processing circuitry 11; 110 and memory 15; 120, wherein the memory comprises instructions, which, when executed by the processing circuitry, causes the system to anonymously track and/or analyse flow or movement of individuals.

By way of example, the anonymization module 12 may be configured to generate a group identifier and/or noise-masked identifier based on the identifying information of the individual by using a hashing function.

FIG. 1B is a schematic flow diagram illustrating an example of a computer-implemented method for enabling anonymous estimation of the amount and/or flow of individual subjects and/or objects, referred to as individuals, in a population moving and/or coinciding between two or more subject states, based on biometric data.

The method comprises the steps of:

-   -   receiving (S1) identifying data from two or more individuals,         wherein the identifying data of each individual includes and/or         is based on biometric data;     -   generating (S2), online and by one or more processors, an         anonymized identifier for each individual; and     -   storing (S3): the anonymized identifier of each individual         together with data representing a subject state; and/or a skew         measure of such an anonymized identifier.

For example, the anonymized identifier may be an anonymized identifier skew measure or other anonymized identifier that is effectively uncorrelated with the population flow.

By way of example, the skew measure may be decorrelating and/or the identifying data is correlated in some way with the population flow and wherein the anonymized identifier is generated with a decorrelation module and/or a decorrelating hashing module.

In a particular example, the anonymized identifier is an anonymous skew measure and the anonymized skew measure is generated based on a stored anonymous identifier skew measure to which noise has been added at one or more moments.

As an example, the anonymized identifier may be generated by adding noise to the identifying data.

By way of example, a compensation term to be added to a population flow estimate and/or necessary information for generating such a population flow estimate is calculated based on one or more generated noise sample(s) used by the method.

For example, any two stored anonymized identifiers or identifier skew measures are not linkable to each other, i.e. there is no pseudonymous identifier linking the states in the stored data.

In a particular example, the anonymized identifier is a group identity, and the group identity of each individual is stored together with data representing subject state; and/or a counter per subject state and group identity.

By way of example, the subject state may be a tempo-spatial location, a computer system state in an interaction with a user and/or a state of health and/or health monitoring of a subject.

Optionally, activity data representative of one or more actions or activities of each individual is also stored together with the corresponding group identity and data describing subject state.

Optionally, the method may further comprise the step of generating (S4) a population flow measure between two subject states, as schematically indicated in FIG. 1C.

FIG. 1D is a schematic flow diagram illustrating an example of a computer-implemented method for generating a measure of flow or movement of individual subjects and/or objects, referred to as individuals, between subject states, based on biometric data.

The method comprises the steps of:

-   -   configuring (S11) one or more processors to receive anonymous         identifier skew measures generated based on biometrically based         identifiers from visits and/or occurrences of individuals to         and/or in each of two subject states, wherein each identifier is         representative of the identity of an individual and includes         and/or is based on biometric data;     -   generating (S12), using said one or more processors, a         population flow measure between two subject states by comparing         the anonymous identifier skew measures between the subject         states;     -   storing (S13) said population flow measure to a memory.

By way of example, the subject states are tempo-spatial locations, computer system states in interaction with a user and/or states of health and/or health monitoring of a subject.

For example, the anonymous identifier skew measures may be counters of group identities.

Normally, a single visitor present in one subject state cannot be reidentified in another subject state with high probability using the anonymous identifier skew measures. For example, he/she cannot be linked through pseudonym and/or through a single entry in a database.

By way of example, the generating step S12 is not based on data already containing some measure of the population flow between the locations on an individual level and/or microaggregated level.

For example, the anonymous identifier skew measures are effectively uncorrelated with the population flow.

Optionally, the population flow estimate is generated based on a linear mapping from the anonymous identifier skew measures.

By way of example, the population flow measure may also be generated based on information about noise samples used to anonymize the data.

As an example, the configuring step S11 includes configuring one or more processors to receive counters of anonymous and approximately independently distributed group identities originating from visits of individuals to each of two subject states; and the generating step S12 includes generating a population flow measure between two subject states using a linear correlation between counters of group identities for each of the two subject states.

By way of example, the subject states may be tempo-spatial locations, and the population flow measure between two tempo-spatial locations may be generated using a linear correlation between counters of group identities for each of the two subject states.

Optionally, an anonymous identifier or identifier skew measure for each subject state may be based on two or more identifier density estimates.

FIG. 2 is a schematic diagram illustrating an example of micro-aggregation of a population into groups. By way of example, a population of subjects/objects under study may be micro-aggregated into groups by using suitable one-way hashing. In short, a basic idea is to use, for each one of a multitude of individuals, identifying information (such as ID #1, ID #2, . . . ID #Y) representative of an identity of the individual, and generate a group identifier (Group ID #1, . . . Group ID #X) based on the identifying information of the individual to effectively perform microaggregation of the population into corresponding groups (Group #1, . . . Group #X).

FIG. 3 is a schematic diagram illustrating another example of micro-aggregation of a population into groups, including the concept of visitation counters. There are visitation counters 16 for each of two or more group identifiers from each of two or more tempo-spatial locations or localities associated with the corresponding individuals. In other words, each of at least two groups (with corresponding group identifiers) has a number (K, L, M) of visitation counters for maintaining visitation counts from each of two or more tempo-spatial locations or localities associated with the corresponding individuals of the considered group.

The estimator 13, also referred to as a population flow estimator, may then be configured to receive counter information from at least two visitation counters, and generate one or more population flow measures related to individuals passing from one tempo-spatial location to another tempo-spatial location.

FIG. 4 is a schematic diagram illustrating how each group of individuals may be associated with a set of spatial locations N, each for a set of points in time.

Optionally, the system 10 comprises an input module 14 configured to, by the one or more processors: receive location data, for each one of the multitude of individuals, representative of a tempo-spatial location, and match the tempo-spatial location of the individual with a visitation counter 16 corresponding to the group identifier related to the individual.

For example, each visitation counter 16 for each group identifier also corresponds to a specific tempo-spatial location.

By way of example, the one or more population flow measures includes the number and/or ratio of visitors passing from one tempo-spatial location to another tempo-spatial location.

In a particular example, at least one of said one or more population flow measures is generated at least partly based on a linear transform of the counter information of two or more visitation counters.

For example, the anonymization module 12 and/or the identifying information representative of the identity of an individual may be stochastic, and the stochasticity of the identifying information (identifier) and/or anonymization module 12 may be taken into consideration when generating the linear transform.

As an example, the linear transform may be at least partly based on a correlation between two visitation counters and from which a baseline corresponding to the expected correlation from two independently generated populations is subtracted.

FIG. 5 is a schematic diagram illustrating examples of subject states such as tempo-spatial location data and useful identifying biometric information (ID).

By way of example, in addition to the temporal aspect (i.e. related to time), the tempo-spatial location data may be related to physical locations such as streets, stores, metro stations, or any other suitable geographical location, and/or virtual locations such as IP addresses, domains, frames, and so forth.

Non-limiting examples of identifying information, also called an identifier, representative of the identity of an individual based on his/her biometric attributes may include and/or be based on at least one of: iris images, facial images, feature vectors, body images, fingerprint and/or gait.

This means one or more of the above information items and/or a combination thereof.

In a particular example, the anonymization module is configured to operate based on a random table, a pseudorandom table, a cryptographic hash function and/or other similar function that is effectively uncorrelated with the aspect of interest the system is designed to study.

As an example, the hashing process may be non-deterministic.

By way of example, it may be considered important that data of at least two individuals is collected or expected to be collected per unique group identifier when such are used. In other words, data of at least two individuals is collected or expected to be collected per unique hash. Alternatively, with a slightly weaker criterion, it may be important that at least two individuals are expected to exist in some population that can reasonably be expected to visit the subject state, e.g. individuals in the city or country of interest where the data is being collected. The range of reasonable identities would be the criterion for anonymity, not the range of reasonable identifiers. For example, the number of possible physical characteristics is generally larger than the range of actual physical characteristics in a country or otherwise defined population.

More generally, to handle the case of noise-based anonymization with a similar criterion, it may for example be important that the probability of correctly identifying an individual should be no higher than 50%, with possible optional exceptions for situations with negligible probability. It may for example additionally be important that the probability of identifying a person is no higher than 50% when given a known subject state and/or reasonably available information about such subject states where a specific person is present. Such knowledge may also be probabilistic. Such probabilities can be calculated in a straightforward manner by the skilled person using analytical or Monte Carlo methods.

When using a noise-masked identifier, it may for example be important that no noise-masked identifier value is linkable to any single person with a probability higher than that of the identifier value belonging to any of the other people in the population. As a consequence, the probability of it belonging to any of the n−1 remaining individuals in the population of n people should ideally be above 0.5. In other words, the probability of identifying an individual should not be above 0.5 and in many cases much lower for it the offer similar protection to k-anonymization for some k=2 or higher. In other words, each of this multitude of identifiers should have a probability of generating the given noise-masked identifier value that is smaller than the sum of the probabilities of generating the noise-masked identifier from each other identifier. If the noise level is too low, the collected data allows the creation of profiles and the method is no longer anonymous due to insufficient data collection.

As an example, the probabilities of generating some specific noise-masked identifier might be 0.6, 0.4, 0.3 and 0.4 for four different received identifiers, with the greatest probability being 0.6/1.7 of the data correctly assigned to a specific individual and thus achieving an anonymity greater than 0.5. It is most often reasonable to assume that that the a priori probability is identical across the population. In other cases, for example if people are identified by facial images and certain types of faces are a priori known to be more likely to be present in the given population, the a priori distribution need to be taken into consideration. This is often a very difficult estimation to make in practice. In such cases, it would be desirable to instead use a decorrelation module and/or have probabilities that have distributions that are sufficiently distributed to leave ample margin for uncertainties in the a priori probability. A completely even distribution across all possible noise-masked identifier values, regardless of received identifier, is not practical, as this would clearly remove any desirable expected skew in the data caused by a particular set of identifiers being used to generate the noise-masked identifiers. In other words, picking a suitable noise distribution becomes a balance between accuracy in the estimation and provided anonymity. There is, however, usually a wide range of choices that can provide both a high degree of anonymity and reasonable accuracy.

It should be noted that the criterion/criteria for anonymity comprises not just the fact that the original identifier can no longer be recreated with a high probability, e.g. to prevent recreation of recognisable facial images etc. This weaker property is true for some salted hashes, temporary random identifiers and a large range of other similar identifiers referred to as pseudonymous. Our invention instead targets a significantly stricter level of anonymization by also preventing the linking of data, for example into profiles, by making an attacker unable to link two or more data points using the stored identifiers on the individual level (while still enabling linking on the aggregated, statistical level). This is also the common definition of anonymization in modern and stricter definition provided by recent scientific and legal definitions of anonymity, such as the General Data Protection Regulation and the recommendation by the EU Article 29 WP Opinion 05/2014 on Anonymization Techniques (with the specific criteria: “is it still possible to link records relating to an individual?”). In contrast, any availability or possibility of non-anonymous data linkable on an individual level, e.g. pseudonymous identifiers, would make the objective trivial to achieve and nonsensical to achieve in the manner described by the invention.

For example, one particular effect of anonymization described herein can be to effectively prevent or significantly hinder any potential profiling of individuals by a third party using the data stored in the system.

As an alternative to method to that of the invention, data can be anonymized after collection while preserving the population flow measure in various ways, for example by microaggregating the population and storing the population flow per group. However, such anonymization requires one or more non-anonymous data collections step. As such, such a system and/or method for population flow measure would not be anonymous, as it would require the collection and storage of personal data from each individual at least for the period separating the visits to the corresponding subject states. This problem is also important enough to be recognized explicitly in legislation, for example in the preamble of the “Proposal for a REGULATION OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL concerning the respect for private life and the protection of personal data in electronic communications and repealing Directive 2002/58/EC (Regulation on Privacy and Electronic Communications)” where it is stated:

“To display the traffic movements in certain directions during a certain period of time, an identifier is necessary to link the positions of individuals at certain time intervals. This identifier would be missing if anonymous data were to be used and such movement could not be displayed.”.

These conclusions did clearly not foresee the invention and clearly states the perceived impossibility in achieving the stated objective with conventional methods while maintaining a proper anonymity.

Such non-anonymous data is not compatible with the data collection envisioned by the invention due to its lack of anonymity in both its collection and storage, making such data types incompatible with the objective of anonymous tracking and/or analysing movement of individual subjects.

The original identifiers might have an uneven distribution. This is the case, for example, by the local geographical bias of biometrically relevant phenotypes in a population. In such cases, the required uniform noise level may be prohibitively high. An improved and proper noise level to guarantee anonymity may need to become dependent on the identifier itself, e.g. adding more noise to identifiers that are more likely to have few neighbors, but this requires an estimation of the underlying distribution of identifiers. Such estimation of the distribution can be very difficult in practice and may also suffer from estimation errors that threaten the anonymity.

We propose, for such cases, an optional additional decorrelation module that is designed to effectively remove any relevant correlations in the anonymized identifiers. For example, it uses a cryptographic hash and/or similar decorrelating function before adding the noise to the resulting decorrelated identifier in the anonymization module. The role of the decorrelation module is to remove any patterns and/or any large-scale patterns in the distribution, which will even out the identifier density, while the anonymity is provided by the noise in the anonymization module rather than the decorrelation. In contrast to the hashing function used to generate group identifiers, the decorrelation module itself does not need to provide anonymous identifiers. Consequently, the decorrelation module may also be truly or probably reversible, such as a reversible mapping or a salted hash that allows data linking and/or a recreation of the original identifier with some probability. Further descriptions of the decorrelation aspect and possible uses of locality-sensitive hashing in a decorrelation module follows the guidelines provided in the related examples below.

In an alternative example embodiment of the decorrelation module, the decorrelating function is instead applied to the noise. This means that a noise source, typically well-behaved such as a Gaussian noise, is transformed into a decorrelated noise, i.e. one with a probability distribution effectively lacking large-scale continuous patterns, for example by applying a hashing function on the well-behaved noise. This decorrelated noise from such a decorrelation module can then be used to simultaneously anonymize and decorrelate the identifying data, for example by adding decorrelated noise and then applying a modulo rspan operation, where rspan is the range of image of the noise source. Care need to be taken in setting the numerical resolution of the noise and/or in designing the hashing method used so that the noise is not perfectly uniformly distributed, since a non-uniform distribution is needed to create the necessary identifier-related skew used by the invention.

As an alternative to the decorrelation module, a decorrelating skew measure can be used. This can for example be any skew measure that does not display large-scale patterns likely to correlate with physical systems, for example by being based on functions such as a randomly initialized table and/or function that is an effectively random identifier-dependent weighting and/or a function only maintaining small-scale patterns unlikely to give rise to significant correlation, such as a modulo operation. The necessary considerations in designing a decorrelating skew measure is largely similar to those in designing a decorrelation module and will be obvious to the skilled person.

Decorrelation of identifying data should be interpreted in context of the skew measure. If the skew measure is likely to be affected by the existing visitation probability patterns in the identifying data, for example with the identifiers affecting a specific identifier density measure on average being significantly more likely to visit a subject state than other identifiers in the population, then the visitation frequency of the identifying data can be considered correlated (with the shape of the skew measure). Hence the correlation can be broken either by breaking their correlation by changing the skew measure and/or the anonymous identifier, while the visitation frequency per subject state and identifier can be considered a given value for a measurement system. For example, since the probability of two completely random functions and/or distribution being significantly correlated is low, a pick of any random mapping would be sufficient to decorrelate them with a high probability.

Very briefly, the theoretical reason for the effectiveness of decorrelation is related to the fact that data with origin in the physical world and/or functions used to model such (e.g. most common and named functions used in engineering) form an infinitesimal and particular subset of all possible functions and have a relatively high probability of similarity and displaying spurious correlations, especially for large patterns. Small-scale physical patterns tend to be at least partly chaotic and effectively random. Further details on such properties can be found in earlier published work by the inventor (e.g. “Mind and Matter: Why It All Makes Sense”). In contrast, an effectively randomly chosen function/distribution from all possible functions/distributions has a much lower, often zero or negligible, probability of displaying such correlations with both functions of physical origin and/or other randomly chosen functions. The avalanche effect gives a different, and yet similar, perspective on the decorrelation aspect. For example, a bent function and/or those fulfilling the strict avalanche criterion can be suitable as a function for decorrelating purposes, while for example functions considered particularly well-behaved and/or functions with low-valued derivatives are usually less suitable due to their approximate linearity correlating with the approximate linearity inherent in most physical systems and models on some scale. Both cryptographic hash functions and random mappings, such as random tables, benefit from these properties but many other functions also possess and/or approximate (e.g. LSH) the relevant properties for the purpose of the invention. Suitable alternatives should be obvious to the skilled person familiar with the theory of hashing, cryptography and compression.

Note that we use adding noise herein in the general sense as the application of any stochastic mapping, not necessarily relying on the addition of a noise term to the identifier. For example, multiplicative noise may also be used. This can still be seen, form the perspective of information theory, as an addition of noise to the information encoded in the data regardless of the form of such an encoding.

The choice of specific hashing and/or noise-masked identifier may be different between the subject states and may also depend on other factors. For example, certain identifiers may be assigned to hashing and others to noise-based masking. Noise may be identifier-dependent and/or dependent on the subject state.

In some contexts, some accessible identifying data is considered an identifier and other potentially identifying data is considered to be additional data unknown to an attacker. For example, precise location data in a public place cannot be used to identify a person unless the attacker is likely to have location data with the same time stamps. If such data is likely to be available to the attacker, it might be suitable to additionally anonymize any additional data together with the identifier. The invention can be used in any such combination. For example, a facial image can be used as an identifier and an anonymized identifier stored by the invention. Together with the anonymized identifier location data is stored in order to analyze travel patterns. This additional location data may then be anonymized separately, for example by quantization of location and time into sufficiently large intervals to be rendered anonymous. The resolution may be different in residential areas and in public spaces, such as retail locations.

In general, the proposed invention can be applied to any sufficient identifying part, i.e. identifying in itself, of the identifying data and the additional identifying data may be anonymized by separate methods. The subject states can then be linked statistically by those identifiers handled by the invention, while the remaining identifying data can be anonymized in a way that does not allow statistical linking of this kind.

According to another aspect, there is provided a system for anonymously tracking and/or analysing flow or movement of individual subjects and/or objects, referred to as individuals.

In this non-limiting example, the system is configured to determine, for each individual in a population of multiple individuals, a group identifier based on a hashing function using information representative of an identity of the individual as input. Each group identifier corresponds to a group of individuals, the identity information of which results in the same group identifier, thereby effectively performing microaggregation of the population into at least two groups.

Noise-masked identifiers perform the same function by adding a random noise with a distribution such that each possible noise-masked identifier value is achievable by a multitude of identifiers.

The system is further configured to keep track, per group, of visitation data representing the number of visits to two or more tempo-spatial locations by individuals belonging to the group. More generally, the system is configured to keep track of a skew measure for two or more subject states.

The system is also configured to determine at least one population flow measure (for the whole population) of the number of individuals passing from a first tempo-spatial location to a second tempo-spatial location based on visitation data per group identifier.

More generally, the system is configured to determine at least one population flow measure (for the whole population) of the number of individuals passing from a first subject state to a second subject state based on the skew measure.

With exemplary reference to FIG. 1A and/or FIG. 11, the system may comprise processing circuitry 11; 110 and memory 15; 120, wherein the memory 15; 120 comprises instructions, which, when executed by the processing circuitry 11; 110, causes the system to anonymously track and/or analyse flow or movement of individuals.

According to yet another aspect, the proposed technology provides a surveillance system 50 comprising a system 10 as described herein, as schematically illustrated in FIG. 6.

FIG. 7 is a schematic flow diagram illustrating a particular non-limiting example of a computer-implemented method for enabling estimation of the amount or number and/or flow of individuals in a population moving and/or coinciding between two or more tempo-spatial locations.

Basically, the comprises the steps of:

S21: receiving identifying biometric data (wherein the identifying biometric data includes and/or is based on biometric data) from two or more individuals;

S22: generating, by one or more processors, a group identity (and/or noise-masked identifier) for each individual that is effectively uncorrelated with the population flow; and

S23: storing: the group identity (or more generally a skew measure per subject state) together with data describing tempo-spatial location; and/or a counter per tempo-spatial location and group identity.

By way of example, the group identity may be generated by applying a hashing function that effectively removes any pre-existing correlation between the identifying data and tendency to be located in one or more of the tempo-spatial locations.

Optionally, the noise-masked anonymization comprises a decorrelation step that effectively removes correlations in the identifier space.

For example, the population of visiting individuals being measured may be an unknown sample from a greater population, with the greater population being large enough that the expected number of individuals in this greater population that would be assigned to each group identity and/or noise-masked identifier is two or more.

The population of visiting individuals can for example be considered a representative sample from this greater population that may implicitly and/or explicitly also be measured through the data collected from the visiting population.

Optionally, the generation of group identity may be partly stochastic each time it is applied.

By way of example, the identifying data may include, per individual, information representative of the identity of the individual based at least in part on biometric attributes of the individual. Non-limiting examples of such biometric information may include and/or be based on at least one of: iris images, facial images, feature vectors, body images, fingerprint and/or gait.

FIG. 8 is a schematic flow diagram illustrating another particular non-limiting example of a computer-implemented method for enabling estimation of the amount or number of individuals in a population coinciding between two or more tempo-spatial locations.

In this particular example, the method further comprises the step of: S24: generating a population flow measure between two tempo-spatial locations using counters of group identities for each of the two tempo-spatial locations.

For example, the generation of the population flow may be based on a linear transform of the visitation counters.

Optionally, the linear transform may include a correlation between a vector describing the population flow per group identity in the first location and a vector describing the population flow per group identity in the second location.

As an example, a baseline is subtracted from the correlation that corresponds to the expected correlation between the two vectors.

For example, the number of individuals in the population may be two or more per group identity.

Optionally, activity data representative of one or more actions or activities of each individual may also be stored together with the corresponding group identity and data describing tempo-spatial location, enabling analysis and understanding not only of tempo-spatial aspects but also of actions or activities of individuals.

FIG. 9 is a schematic diagram illustrating an example of movement or flow of one or more individuals from location A to location B. For example, this may involve individual subjects and/or objects moving from one location to another, and being recognized, e.g. by cameras or by other means, e.g. people being recognized through facial recognition, fingerprint and/or iris scan and/or other biometric information.

FIG. 10 is a schematic diagram illustrating an example of movement or flow of users from one virtual location such as an IP location to another virtual location. This could be an individual user moving from one Internet domain to another Internet domain, such as from IP location A to IP location B, and e.g. being recognized through facial recognition, fingerprint and/or iris scan and/or other biometric information.

By way of example, the biometric information may be obtained, e.g. by using well-accepted technology for extracting fingerprints, facial data and/or iris data through a laptop, personal computer, smart phone, tablet and so forth.

FIG. 12 is a schematic flow diagram illustrating an example of a computer-implemented method for generating a measure of flow or movement of individual subjects and/or objects, referred to as individuals, between tempo-spatial locations, based on biometric data.

Basically, the method comprises the steps of:

S31: configuring one or more processors to receive counters of anonymous and approximately independently distributed group identities, wherein the counters are based on biometric data, originating from visits of individuals to each of two tempo-spatial locations;

S32: generating, using said one or more processors, a population flow measure between two tempo-spatial locations using a linear correlation between counters of group identities for each of the two tempo-spatial locations; and

S33: storing said population flow measure to a memory.

For a better understanding, various aspects of the proposed technology will now be described with reference to non-limiting examples of some of the basic key features followed by some optional features.

The invention receives some identifying biometric data that is able to, with a high probability, uniquely identify an individual and/or personal item of an individual. It may optionally be continuous data, for example biometric measurements. It may also be any combination and/or function of such data from one or more sources.

In preferred examples, the invention comprises an anonymization module, that comprises a (anonymizing) hashing module and/or a noise-based anonymization module.

Examples—Hashing Module

Some aspects of the invention involve a hashing module. A hashing module, in our sense, is a system that is able retrieve identifying data and generate some data about a person's identity that is sufficient to identify the individual to some group that is substantially smaller than the whole population, but not sufficiently small to uniquely identify the individual. This effectively divides the population into groups with one or more individuals, i.e. it performs an automatic online microaggregation of the population. These groups should ideally, but not necessarily, be independent from the population flows being studied in order to simplify the measurement. In other words, we seek to divide them in such a way that the expectation of the flow of each group should be approximately the same. In particular, the variance in any pair of groups should be approximately independently distributed. Expressed differently, we would like to be able to consider the group as an effectively random subset of the population in our statistical estimates. For example, this can be achieved by applying cryptographic hash or other hash that has a so-called avalanche effect. A specific example of a suitable hash, if locality-sensitivity is not desired, is a subset of bits of a cryptographic hash, such as SHA-2, of a size suitable to represent the desired number of groups that correspond to the number of individuals we would like to have per group. Padding with a constant set of bits can be used in this example to reach necessary message length. However, this specific example of hash brings some overhead to the computational requirements and hashing modules better adapted for this specific purpose can also be designed, as the application herein does not necessitate all the cryptographic requirements.

Preferably, any correlation, whether linear or of another type, that could significantly bias the resulting measure from the system should effectively be removed by the hashing module. As an example, a sufficient approximation of a random mapping, such as a system based on block ciphers, chaotic systems or pseudorandom number generation, can achieve this goal. In the minimalistic extreme, a simple modulo operation may be sufficient if this is deemed unlikely to create correlated identities.

If the identifiers do not contain such correlation, e.g. if they are randomly assigned, then the hash does not benefit from being decorrelating, as any group assignment will be effectively random even without it.

In some aspects of the invention, depending on the required conditions for anonymity, the amount of groups may be set so that either an expected two or more people from the population whose data has been retrieved or two or more people from some greater population, from which the population is effectively a random sample, is expected to be assigned to each group. The invention allows an efficient unbiased estimation in both of these cases as well as more extreme anonymizing hashing schemes with a very large number of individuals per group.

The hash key, representing a group identity, can be stored explicitly, for example a number in a database, or implicitly, for example by having a separate list per hash key.

In other words, the hashing module takes some identifying data of a population and also generates, for example, effectively (i.e. an approximation sufficiently good for the purposes herein) randomly sampled subgroups from the whole population. The hashing module as described herein has several potential purposes: ensuring/guaranteeing the decorrelation of data from the population flow (i.e. using a group identity that has, possibly unlike the identifying data, effectively no correlation with the population flow) and anonymizing the data by microaggregating it while preserving some limited information about the identity of each individual. In some embodiments of the invention the hashing module may also, as described in more detail below, serve to preserve limited information about the data itself by using a locality-sensitive hashing.

For these aspects of the invention, the statistics collected per group identity are instrumental in generating the population flow statistics for the (whole) studied population comprising a multitude such groups. The purpose of the invention is not to measure the differences between the groups as such, and in particular if the decorrelation is intentionally generating rather meaningless subdivisions of the population due to the effective removal of any potential correlations between members of the group.

As an example of suitable hashing modules, divisions into group based on continuous ranges of one or more of many meaningful variables, such as yearly incomes, home location, IP-range or height are unsuitable criteria in the preferred embodiment, as this is likely to results in different expected population flow patterns for each group that would need to be estimated for the overall population flow to be measured. On the other hand, we could use, for example, a limited number of bits from a cryptographic hash or a random mapping from an initial grouping into sufficiently small ranges of any of these criteria(s) in order aggregate an effectively random selection of such small groups of continuous ranges into a larger group. In other words, we divide the identifiers into many small continuous ranges and define our groups as some effectively random selection of such continuous ranges such that each continuous range belongs to a single group. In this way we would divide the population into a set of groups that are effectively indistinguishable from a random subset of the whole population, as any large scale patterns are effectively removed. Alternatively, we could save a cookie on the user's computer that is a pseudorandomly generated number in a certain range that is small enough that several users are expected to get the same number. Alternatively, these continuous ranges could for example also be replaced with otherwise defined continuous n-dimensional extents and/or be non-uniquely mapped to a certain group with a similar effect for the purpose of the invention, i.e. that of creating a suitable locality-sensitive hashing.

Stochastic group assignments will not prevent the hashing method from being applied and can also add a meaningful layer of extra anonymity. Biometric data usually contains some noise level due to measurement error and/or other factors that makes any subsequent group assignment based on this data a stochastic mapping as a function of the identity. Stochastic elements can also be added on purpose. For example, the system may simply roll a dice and assign an individual to a group according to a deterministic mapping 50% of the time and assign the individual to a completely random group the other 50% of the time. The data can still be used in our system as long as the distribution of this stochastic assignment is known and/or can be estimated. Further, the simple dice strategy above will be roughly equivalent to a k-anonymity with k=2 in addition to the anonymity already provided by the grouping.

Examples—Noise-Based Anonymization

Some aspects of the invention comprise a noise-based anonymization module. A noise-based anonymization module generates a new noise-masked identifier based on the identifying data. Such a module uses a stochastic mapping where the output is irreversible due to the added noise rather than by limiting the amount of information stored. In other words, the signal is kept below the identifying limit even if the total amount of information used to store the signal and noise would hypothetically be greater than this limit. Any stochastic mapping can be used such that linking a noise-masked identifier to a specific identity is unlikely. In contrast to a hashing module, the noise-masked anonymization module produces an output with sufficient information content to identify a unique person. However, some part of this information is pure noise added by the anonymizer and the actual information concerning the identity of a person is below the threshold required to link data points on the individual level with high probability. Although a hashing module is preferable in most cases, the noise-masked identifier might match more naturally into noisy identifiers of various kinds and also prevents certain deanonymization in some cases where an attacker knows that the person has been recorded.

Noise can be any external source of information that can be considered noise in the context of the invention and does not imply a source of true noise. For example, time stamps or values from some complex process, chaotic systems, complex systems, various pseudorandom numbers, media sources and similar sources whose patterns are unlikely to be reversible could be used. From anonymity perspective it is important that this noise cannot easily be recreated and/or reversed and the statistical purpose of the invention additionally requires that it can be described by some distribution and does not introduce significant unwanted correlation that alter the statistics.

FIG. 13 is a schematic diagram illustrating an example of how an identifier skew measure can be made anonymous by adding noise at one or more times and how this can generate a bias compensation term. In this example, visitation counters are used for subject state A and B, respectively. There population counters are randomly initialized, e.g. before the data collection starts. A bias compensation term is calculated by estimating the population flow from A to B resulting from spurious correlations in the initialization, which can be removed from the population flow estimate in the future in order to lower the variance of the estimate. To further mask the initialization, an additional small noise may optionally be added to the compensation term at the cost of a slightly increased variance in the population flow.

FIG. 14 is illustrating an example of noise-masking anonymization. It shows the probability density function of the noise-masked identifier given some identifier. The probability density functions, in this example approximately normally distributed around the identifier, for two different identifiers are shown. Not all possible input values may correspond to an individual in the population and/or memory. Where the probability density functions from different identifiers are overlapping, the original identity generating that noise-masked identifier may not be known with certainty. Reidentification using a specific noise-masked identifier becomes less probable as more overlap from the probability density functions of various identifiers is provided for that specific noise-masked identifier, for example by having more identifiers in the population and/or memory.

Examples—Anonymized Identifiers

For example, an anonymous identifier is herein considered a group identifier and/or a noise-masked identifier.

In other words, an identifier herein is in the general sense as a specific sample of identifying data of any type and not necessarily an enumerable that a more narrow definition of the concept could suggest.

By way of example, people that are assigned to the same group by the hashing module may be seen as a hash group.

Examples—Skew Measure

For example, skew of data herein refers to how some particular data is distributed compared to the expectation from the generating distribution. The skew measure is some information describing the skew of the collected data. In other word, the invention measures how the actual identifier distribution differs from the expected identifier distribution, for example the distribution if all individuals were equally likely to visits both subject states. It is usually encoded as one or more floating point or integer values. The purpose of the skew measure is to later be compared between subject states in order estimate how much of this skew is common between two subject states. A large number of varieties of skew measures will be obvious to the skilled person. Practically any skew measure can be used in the invention, although some skew measures preserve more information about the data skew than others and thus are likely to provide a better estimate of the skew. Note that a skew measure does not necessarily imply that the generating distribution is known, i.e. that enough information has/have been collected about the expectation of the generating distribution in order for the skew to be calculated from the skew measure. However, if the underlying distribution would later become known the skew measure would already contain the information necessary to estimate the skew the data. That said, the result generating distribution will be trivial to estimate if the identifiers are decorrelated, e.g. using a decorrelation module.

The most elementary example of a skew measure is to keep a list of the original visiting group identities or noise-masked identities, together with any associated additional data, which offers anonymity but may be inefficient in terms of storage space as they contain redundant information. However, in some cases, keeping such original anonymized identities allows a better optional post-processing, for example removal of outlies, as well as greater flexibility in changing the skew measures ad-hoc for various purposes.

Another example of a simple skew measure is a visitation counter. Such a visitation counter is counting the number of identities detected at each subject state for each hash group. It could, for example, be a vector with the numbers 5, 10, 8 and 7, representing the number of visiting identities assigned to each of four group identities at a certain subject state.

More generally speaking, a skew measure may for example consist of two or more sums and/or integrals over convolutions of: some mapping from the space of anonymized identifiers to a scalar value; and the sum of Dirac or Kronecker delta functions of the anonymous identifiers visiting a subject state. In other words, we measure the identifier distribution in two different ways. In the specific case where the anonymous identifiers are discrete, such as an enumeration, and the respective mappings are Dirac delta d(i) for i=1:n, this is equivalent to a visitation counter. In other words, a skew measure is a generalization of the anonymous visitation counter. In other words, the skew measure is two or more counts of the number of detected anonymous identifiers from some defined subset of the set of possible anonymous identifiers, where the count may be weighted by any function dependent on the anonymous identifier. Expressed differently:

sum_i f(x_i)

where x_i is a anonymous identifiers visiting a subject state, i is some index of all anonymous identifiers visiting a subject state and f(x) is some mapping from the space of anonymous identifiers to (not necessarily positive) scalar values.

The above sum can be seen as a density estimate of the visiting subpopulation. Since it estimates the distribution of the actual visiting identifiers, which is a finite and known population rather than a proper unknown distribution, we also use the less common but more precise term “density measure” herein to describe such quantities. The simplest density measure is a count of total visits, corresponding to equal weighting across identifiers, which could be used together with another density measure to arrive at a very simple skew measure. In the preferred embodiment a hundred or more density measures would be used as a vector-valued skew measure.

Alternatively, a skew measure may consist of information representative of one or more difference between such density measures. For example, given two counts we may simply store the difference between them as a measure of the skew.

In other words, the skew measure is generally a vector-valued data that consists of information representative of the skew of the identifiers in comparison with the expected distribution of all identifiers sampled from some larger population.

This information may be encoded in any way. Although the method could theoretically work with only a single difference between two density measures, it is most often preferable to rely on as large a number of density measures as the desired level of anonymity allows in order to reduce the variance of the population. In the preferred embodiment of the hashing module, 10—1 000 000 000 density measures are used, depending on how large the group of potential visiting identities are and the expected size of the dataset. From another perspective, reaching an average anonymity level roughly equivalent to k-anonymization with k=5 is almost always desirable and a stricter k=50 or more is recommended in most cases.

A key realization to the utility of the method is that the flow measures can surprisingly reach a very low variance using a large number of density measures and/or other information-rich skew measures, while still preserving the anonymity of the individuals. An extremely low number of density measures will be impractical for the stated purposes due to prohibitive variance, but this disadvantage disappears as the skew information encoded in the skew measure, e.g. the number of density measures used, increases.

For example, a visitation counter for two or more tempo-spatial locations, also referred to as spatio-temporal locations, may be used. This keeps track of how many times people from each of two or more hash groups have been detected at a tempo-spatial location, for example: a certain web page, a specific street, in a certain store etc, at a certain time (recurring or unique).

A more general skew measure than visitation counters is, as mentioned above, a set of identifier density measures, also called density measures herein. A density measure indicates the density of identifiers in the data according to some weighting. For example, a skew measure could be a set of Gaussian kernels in the space of possible identifiers. Specifically, the density measure associated with each kernel may include sums of the weighted distances, i.e. a Gaussian function of the distance, from the center of the kernel to each anonymized identifier. Two or more such density measures from different Gaussian kernels, or one or more comparisons between such density measures, would then represent a skew measure. An identifier density measures can measure the identifier density of identifying data and/or anonymous data.

Such density measures can be correlated between the two points just like the visitation counters used in some of the specific examples described herein in order to estimate the population flow. This is true even if the density measures are different, for example if different density measures are used in point A and B. For example, the same method that may be used for visitation counters, i.e. of establishing a minimum and maximum expected correlation depending on the number of coinciding visitors using Monte Carlo and/or analytical estimation.

For the purpose of providing anonymity it is important that this anonymization into an anonymous skew measure takes place effectively online (or in real-time and/or near real-time), i.e. continuously with but a short delay between the acquiring of the identifier and the generation and/or updating of the skew measure. In the preferred embodiment the hashing takes place inside a general-purpose computer being located in a sensor system or a general-purpose computer immediately receiving this value. The value should not be able to be externally accessed with reasonable effort before being processed. Immediately after processing the identifier should be deleted. However, if needed the data may be batched at various points and/or otherwise handled over some small time interval (for example transmission in nightly batches) in the preferred embodiment if this extended type of online processing is necessary for reasonable technical requirements and if it is also not considered to substantially weaken the provided anonymity of the subject. In contrast, offline methods are generally applied after the whole data collection has been completed. Such offline methods cannot be considered anonymous due to the storage of personal data.

Subject States and Visits

The group identities, noise-masked identities and other skew measures, for example visitation counters, and/or any data tied to group identities and/or noise-masked identities, may optionally be modified in any way, for example by removing outliers, filtering specific locations, filtering group identities that coincide with known individuals, or by performing further microaggregation of any data.

The spatial aspect of a tempo-spatial location above can also be virtual extents of IP addresses, domain names, frames or similar aspects describing the connection between a person to part of the state of an electronic device and that describes the state of his interaction with it. These aspects are also covered by the wider definition of subject state.

Subject state is any description of a person's tempo-spatial location, health, actions, economy, behaviour, physical attributes, clothing, position, assigned class by a classifier, immediate environment and/or state of interaction with a computer, webservice and/or other service and/or other meaningful description of the person. In other words, the subject state is some category describing the person either in him/herself of in relation to the interaction with some other entity.

A visit is the connection of an identifier to a subject state. For example, it could be an identifiable person being detected in a specific area at a certain time, an IP address filling a web form or a subject being tested for a disease.

Tempo-spatial location is any extent, not necessarily continuous, in space and/or time. It can, for example, be the number of visits to a certain metro station on any Friday morning. The count can be any information about the number of individuals. For example, it can simply keep a Boolean value that keeps track of whether at least one individual has visited a tempo-spatial location or not. In another example, it can keep track of how many more individuals from a certain group have visited compared to an average across all groups. It can also keep track of more specific location data, for example specific geocoordinates and time stamps, that is at some later point aggregated into larger tempo-spatial locations. This specific data is then considered keeping track also of visits to the larger locations implicitly. One example of a possible visitation counter is illustrated in FIG. 4.

Tempo-spatial location and tempo-spatial locality can generally be seen as synonyms in the context herein and can include any defined extent space, time and/or spacetime.

Subject states can also be defined with fuzzy logic and similar partial membership definitions. This will generally result in partial visits rather than integer values and is generally compatible with the invention.

Examples—Anonymous Population Flow Estimation

The flow measurement uses the data from the skew measure to measure the flow of individuals from one subject state (A) to another subject state (B). Since each hash group and/or density measure represents a multitude of individuals, we cannot know precisely how many people from a certain group or population present in A that were also present in B. Instead, the invention exploits higher order statistics to generate noisy measurements.

The measure of the flow is an estimate of the amount of people that visit both subject state A and B in some way. For example, it may be the amount of people transitioning from state A to B and/or the percentage of the number of people transitioning from A to B. It can also be, for example, to measure the amount of people visiting A, B and a third subject state C (where the people also visiting C can then be seen as a subpopulation for the purposes of the invention). In another example, it can be the number of people visiting A and B, regardless of which subject state is visited first. There are many varieties of such measures available. The number of people visiting A together with the number of people visiting B, independent of any correlation between the corresponding identities between the subject states, is not herein considered a population flow estimate but rather two population estimates corresponding to two locations.

The identities of subjects visiting a subject state will be skewed compared to the estimated visitation rate from all individuals in some hypothetical larger population due to the fact that the visiting individuals form a subset of all individuals in the larger population. If the same individuals are visiting state A and B, this can be measured using the corresponding skew measures. Such a measure is complicated by the fact that we do not necessarily know the theoretical underlying distribution of visitors to A and B. For example, A and B may display similar data skew due to phenotypes in the geographic area. Such correlations will be difficult or impossible to isolate from the coinciding visitors.

Some types of identifiers are, truly and/or approximately, randomly and independently assigned to individuals in a population, e.g. if a random number is picked as a pseudonymous identifier. Such identifiers will display no data skew between A and B due to causes other than that of the individuals coinciding between the locations. In other words, the estimated distribution of the hypothetical larger population is known. In other words, the identities are then effectively independently sampled for each individual and the distribution of the assignment is known. This means that the precise expected distribution of identifiers in A and B is known. Since the expectation is known, the skew from this expectation can also be estimated without need for data collection and with no resulting bias. Moreover, the independence of the identifier assignment also means that a skew measures such as the specific ones discussed above, i.e. weighted sums and integrals that depend linearly on each detected identity, will become analytically derivable mappings of the number of coinciding individuals.

For example, practically any scalar value that depends linearly on the skew measure can be used for constructing a flow estimate if the mapping is linear. It will also be straightforward to estimate this linear value, e.g. using Monte Carlo methods or analysis, for the specific case of a some maximum correlation between individuals in subject state A and B respectively as well as for the specific case when the individuals in the two subject states are different individuals. Due to the independence of the identifiers the flow estimate can easily be constructed using a linear interpolation between these two values. The preferred embodiment uses a correlation between two identical types of skew measures for simplicity.

Note that the population flow measure, depending on its form, e.g. questions such as if it is stated as percentage of visitors and/or total amount, might depend on the total or relative number of individuals in A and in B, which in this case might also need to be collected for each subject state.

Any nonlinear case would require more analytical footwork in its design and might be computationally more expensive, but is otherwise straightforward and will be equivalent in function. The preferred embodiment is linear due to its simplicity and efficiency.

Many types of identifiers, however, are not even approximately randomly assigned, for example home address geolocation data. They may for example correlate with the frequency to visit a subject state a priori. In these cases, the invention can optionally use, for group identifiers, a decorrelating hashing module and, for the noise-masked identifiers, a decorrelation module, in order to remove any unwanted correlations present in the identifier distribution and make the identifiers approximately independently generated from each other and functionally equivalent to a random and independent assignment. Once this has been done a flow measure, such as a linear transform, can easily be constructed without prior knowledge about the initial distribution as described above.

Concrete examples and preferred embodiments of the generation of population flow estimates can be found in the various examples below.

In the preferred embodiment, a baseline is established by estimating, for example by dividing the total number of visits for all groups in the visitation counter with the number of groups, the expected number of visits per group. Such an expectation baseline may also contain a model of the bias, e.g. in case the expected bias by sensor systems and/or similar that are used in directly or indirectly in generating the anonymous identifier can be calculated by depending on factor such as location, recording conditions and time of recording. Additionally, the baseline may be designed taking into consideration population behavioural models, for example: the tendency for repeated visits to a location per individual and/or the behaviour of visitors that are not recorded for some reason. By subtracting this baseline, the preferred embodiment arrives at the skew of the data per group. By way of example, skew of data may refer to how some particular data is distributed compared to the expectation from the generating distribution.

For example, the correlation between the variances per group in A and B represents the skew of the joint distribution. A careful consideration by the inventor reveals that a measure of the number of individuals can be achieved by exploiting the fact that the group identity and probability of an individual to go from A to B can effectively be considered independent and identically distributed, which may be guaranteed through the design of the hashing module and/or decorrelation module. For example, by relying on the assumption of the independence attribute and by using: knowledge of the stochastic aspect of the distribution of the hashing module (which may include models of any sensor noise, transmission noise and other factors involved), if applicable; and a behavioural model that describe the distribution of the number of visits per individual etc, we can create a baseline skew of the joint distribution (for example a Pearson correlation coefficient identical to 0) that would be expected if the two populations visiting A and B were, from a stochastic perspective, independently generated. We can also, using a similar behavioural model and/or knowledge of the stochastic distribution in the hashing module, estimate the skew of the joint distribution in case the two populations consisted of exactly the same individuals (for example a Pearson correlation coefficient equal to 1). For example, such a skew for perfectly coinciding populations may be adjusted based on models of sensor noise, wherein the sensor noise model can be dependent on other factors, such as sensor noise models, location, group identity, identifier noise and/or knowledge of the stochasticity in the hashing process. In a simple example with homogenous groups, comprising a hashing module with 50% chance for consistent group assignment for each individual (with otherwise random assignment between all groups) could double the population estimate for the same skew compared to the estimate for a 100% accurate hashing module.

A statistical measure of the number of individuals can then be generated by for example performing a linear interpolation between two such extremes based on the actual skew as measured by comparing the skew measures. Note that these steps are only an example, but that the independence assumption will result in the population flow measurement being representable as a linear transform, such as the one indicated in some aspect described herein. Various specific embodiments and ways to design specific such embodiments can be arrived at by the skilled person from this and other examples and descriptions herein.

In certain cases, the identifiers are decorrelated already from the beginning. This may, for example, be the case with unique identifiers assigned through biometric templates with random unique identifiers, where the unique identifier is a truly random or approximately random number generated for each biometric template.

The complexity in generating such a measure without the decorrelation assumption made possible by the inherent design of the hashing module, and with noise-masked identifiers by the decorrelation module, would in many cases be prohibitive. Note that this simplification does not only simplify the precise design process of the embodiments, but will also result in cheaper, faster and/or more energy efficient methods and systems due to the reduced number of processing operations being reduced and/or simplification in the hardware architecture required.

The groups in this example do not necessarily need to be of the same distribution (for example having identical estimated group sizes) a priori. With different expected group sizes, the population flow estimation will affect the estimated value per group counter and the (normalized) correlation in a straightforward manner. Any related estimation of variance for the population flow measure might become more convoluted, for example as any Gaussian approximation of the distribution of correlations might be invalid if the group differences are large.

Likewise, the density measure and/or other skew measures may differ in a multitude of ways.

More complex subject states may for example also be defined in order to calculate refined population flow estimates. An identifier skew measure, such as a group identity may for example be stored together with subject state as above (i.e. with an “original” subject state) and the ordering of the visit (i.e. an ordinal), which then allows calculation of the population flow from original subject states before and/or after each particular visit of the subject to an original state. This can from the perspective on the invention be viewed as an aggregation of many individual new subject states (i.e. one subject state per ordinal and original subject state) into a larger subject state (i.e. states before and after a particular visit) together with the aggregation of population flow estimates into larger population flow (i.e. the population flows from all subject states before a particular visit x in state B, summed over all recorded visit x in state B). This more complex calculation allows the calculation of the population flow to B from A with a lower variance, but the larger number of subject states leads to a smaller number of anonymized identities in each subject state, which might weaken the anonymity provided by the invention.

Examples—Locality-Sensitive Hashing

Correlations in the anonymized identifiers can usually, but not always, be avoided through decorrelation. A particular case of where it cannot usually be avoided is with certain noisy continuous identifiers. For example, continuous measurements of biometric data can be hashed using a locality-sensitive hashing (LSH), which allows continuous measurements that contain sensor noise to be used in microaggregation for our purposes. Such a hash function can be approximately and/or effectively, but not perfectly, decorrelating. Any choice of a specific LSH necessitates a balance between its decorrelating properties and its locality-preserving properties. Even if such hash is largely decorrelating the data it is still likely to preserve some remaining small bias in the distribution of the hash resulting from any correlation between biometric measurement and a priori tendency to visit a location (if such correlations are at all present in the original continuous distribution). A term in the baseline (“err”), further elaborated on below, may then be used as a compensation of such remaining correlations. Note that we do not strictly use decorrelation such as that from the avalanche effect in this setting but assume that small scale correlations resulting from the locality-sensitivity have a small effect on the resulting statistics (in other words, the correlations are effectively removed). In particular, any significant correlation between the data and a priori tendency to visit a location is likely to be a large-scale pattern. LSH-based hashing modules are not limited to continuous data, but could be utilized for other data, for example integer values, as well.

As a particular example of LSH, a locality-sensitive hashing may be designed by splitting the space of continuous identifier values into 30 000 smaller regions. A cryptographic hash, random table and/or other method may then be used to effectively randomly assign 30 regions to each of 1000 group identifiers. This means that two effectively independently sampled noisy continuous identifiers received from an individual have a large probability of being assigned to the same group. At the same time, two different groups may be likely to have a negligible difference between them due to each group consisting of 30 independently sampled regions of the feature space. The decorrelation will generally be effective if the regions are much smaller than the correlation patterns of interest. For many well-behaved continuous distributions, both the noise resistance, i.e. robustness of the variance of the population flow estimate to the presence of noise such as identifier/sensor noise etc, and the effective decorrelation of the groups can be achieved at the same time. Since an individual may be assigned to different regions solely due to the noise in the identifying data it may be beneficial to compensate the estimation for the resulting stochasticity in the group identity assignment.

As an example of the above concepts concerning LSH, people over 120 cm of height may be significantly less likely to enter a toy store than those under 120 cm, while the corresponding a priori difference between people whose height is 119.5-120 cm and people between 120.0-120.5 cm of height is likely to be negligible and hence approximately uncorrelated.

Note that the decorrelation module might also use an LSH as described above in order to produce a locality-preserving identifying value with effectively no correlations of the type described above. The difference compared to a anonymizing module is that the number of possible decorrelated identifier values is sufficiently large for an individual to be uniquely identified from the value. For example, the collision probability of a decorrelating hash may be low. There might be some resulting probability of failing to identify a person correctly, but not sufficiently to be considered anonymizing (i.e. the decorrelation module decorrelated but does not anonymize). Stochasticity then becomes a necessary additional anonymization step to the LSH in order to protect the personal identify.

It can be noted that for large number of sample and a large number of possible hashes the correlation of two independent populations are approximately normally distributed. This makes it easy to also present confidence intervals for generated measures if desired.

Examples—Behavioural Models

The population flow may optionally be modified by a behavioural model in order to arrive at derivative statistics, such as the flow of unique individuals if visits can be repeated at each location. Such a behavioural model, could for example estimate the expected number of revisits per individual. Such a behavioural model could also, for example, be estimated together with the population flow iteratively in an estimation-maximization process where the population flow and behavioural models are repeatedly updated to improve the joint probability of the observed identifier distributions.

Example Implementation

In an example preferred embodiment a server in the example system applies a hashing module to received identifiers and stores an integer between 1 and 1000, effectively random due to the avalanche effect. Assuming the number of individuals to be 10000 at A and B respectively and assuming individuals only go once per day in one direction and with no other correlation between the corresponding populations at A and B, the expected mean for both points is 10000/1000=10 individuals per group. We may encode the measured number of individuals per group in integer valued vectors n_a and n_b respectively. We can now calculate the unit length relative variance vectors v_a and v_b as v_a=(n_a−10)/norm(n_a−10) etc (where the function norm(x) is the norm of the vector and subtracting a scalar from a vector signifies removing the scalar value from each component). Assuming that every individual passing A also passes through B in a day we arrive at a perfect correlation, E[v_a*v_b]=1 (where * is the dot product if used between vectors and E[ ] is the expectation). Instead assuming that the population in A and B always consist of different individuals, we can instead estimate a baseline as E[v_a*v_b]=0, here using the uncorrelated assumption made feasible due to the use of a hashing module. Assume now that the number of individuals at B, c3, consist of two groups of individuals, c1 (with relative variance vector v_a1) coming from A and c2 (with relative variance vector v_a2) not coming from A. The expected correlation in this case becomes E[c3*v_b*v_a1]=E[(c1*v_a1+c2*va2)*v_a1]=c1. This means we can measure the expected number of individuals going from A to B as nab=v_b*v_a1*10000. Assuming we measure a scalar product of 0.45 between v_b and v_a in this example we arrive at a measure of 4500 individuals, or 45% of the individuals in B, coming from A. In other words, we arrive at an unbiased measurement using strictly anonymous microaggregated data that can be implemented as a linear transform through the use of a decorrelating hashing module. The data generated by the hash module in the example may be considered anonymous and uploaded to any database without storing personal data. The described calculations herein can then preferably be performed on a cloud server/database through the use of lambda functions or other such suitable computing options for the low-cost calculations required to perform a linear transform.

The counters and/or correlation may be normalized or rescaled in any way as part of generating the estimate. The various calculations should be interpreted in a general sense and can be performed or approximated with any of a large number of possible variations in the order of operations and/or specific subroutines that implicitly perform effectively the same mapping between input and output data as the calculations mentioned herein in their most narrow sense. Such variations will be obvious to the skilled person and/or automatically designed, for example by compilers and/or various other systems and methods. In case of a slightly imperfect hash function the resulting error in the above assumptions can be partly compensated for by assuming E[v_a2*v_b]=err, where err is some correlation in the data that can be estimated, for example empirically by comparing two different independent samplings from the population (i.e. measuring traffic at two spots that can have no correlation with each other). The expectation then follows the following equality: c1=E[(c1*v_a1+c2*va2)*v_b]−err. This err term may for example be used as a baseline or part of a baseline.

Note that this simple case is slightly more complex when the number of people in A is greater than in B. Even if all people in B come from A we would expect a less than ideal alignment in the group distribution. This maximum expected scalar product could easily be estimated from the total number of visits to A and B. In these cases the linear transformed used to arrive at the estimate becomes a function of the total number of visits in A and B, respectively.

If a noise-masked identifier is used, we could simply divide the identifier space into a number of areas and calculate the density estimation for each. A calculation can be performed for these density measures that is analogous to the visitation counters above.

Examples—Anonymizing Skew Measures

An issue that can arise using any skew measure is that the subject states are initially weakly populated by visits and that a probabilistic linking of an identity to a multitude of data points is then possible for an attacker if the identifier is known.

For example, a visitation counter might have a group with a single visit to subject state A, then it might be reasonable to assume that an individual is the only registered individual from that group in the dataset or, more specifically, reasonable to assume that he/she is the sole individual in A.

Alternatively, it might for example be reasonable to deduce the group identifier from sparsely populated data in a given location, e.g. a known home address. It can then be checked against and a work address. In that case it might be possible to infer that he/she was indeed present at location B with a high probability. This specific case can be countered by only storing the skew measure in location A and generate the population estimate online, i.e. updating it with every single visit to B using the skew measure from A, but without storing the skew measure from B. However, this method will be ineffective if the population flow estimate from B to A also needs to be calculated.

A solution for these weakly populated states, as well as a potential anonymization solution in its own right, is to use anonymizing skew measures.

Anonymizing skew measures work by adding a degree of noise to the stored skew measure. This can for example be done before starting the data collection, as well as at during any number of moments during the collection. This noise could potentially bias the population flow estimate. The bias can be compensated for by calculating the resulting bias based on the estimate of the noise. More problematic is that this will also increase the variance of the population flow estimate.

An optional improved mechanism can be designed. In this mechanism, the bias generated from the specific noise sample used, and/or other information suitable for generating such a bias based on the specific noise sample, is also generated. For example, a random number of “virtual” visits per group identifier can be generated and prepared for addition to a visitation counter. The total population flow estimated from A to B by the spurious correlation of all such virtual visits in A and B is also stored as a bias term, as well as the number of total virtual visits per location. Since the correlation from the actual generated virtual visits is precisely known at the moment they are generated, it can also be calculated and removed precisely through the bias term. This method significantly reduces the variance in the data, although some cross terms caused by spurious correlations between actual visits and virtual visits may remain as a contributor to the variance. Instead of storing a bias term directly, any information necessary for generating such could alternatively be stored. If too much information about the noise is stored, the data might be deanonymized. However, the necessary bias term is a single value, while the noise is typically vector-valued, so there are many possible ways to store sufficient data without storing enough information about the noise to deanonymize the data.

In the particular illustrative example of a visitation counter encoded in a vector v_a and v_b, we have:

v_a=f+a+n_a

v_b=f+b+n_b

where a and b are the visits unique to subject state A and B, respectively, and f the common population. n_a and n_b are noise terms.

In this example, various measures of population flows are related to the following value:

E[v_a′*v_b]=E[f′*f]+2E[(a+b)′*f]+2E[a′*b]−2E[(a+f)′*n_b]+2E[n_a′*(b+f)]−n_a′*n_b′

where * is the dot product and ′ is transpose of the vectors.

Note that if the noise level is substantial the direct calculation of the noise terms rather than its estimation might reduce the variance significantly and so in particular if the variance in the noise is larger than the variance in the other terms, for example if the visitations counters are sparsely populated. The mixed noise/data terms such as a′ *n_a can also be calculated precisely if the noise is added after the data, or partially calculated and partially estimated if the noise is added at some point during the data collection.

As a final security measure, a small amount of noise may be added to the compensated bias term generated from the virtual visits. Usually a very small random number, such as between 0 or 1, is sufficient to mask any individual contribution to the skew measure even in exceptional cases where such can be isolated from the skew measure Such noise to the bias term might prevent reconstruction of the skew measure noise when a larger number of subject states are used. Optionally, the noise is sufficiently high that no precise number of visits for any identities is deducable with a probability higher than 0.5. For example, if the noise is generated based on a random integer number of visits per group identifier, the probability of any such specific number of visits per group identifier should then ideally be 0.5 or less.

Practical memory storage limitation usually limits the noise range that can be used. However, this is more of a theoretical concern if the probability is higher for generating small values and progressively smaller for larger noise additions. This lacks any effective maximum value, except with a probability that is negligible. For example, probability density functions exponentially decaying with the magnitude of the noise might be used. Such noise preferable has an expectation value of 0, in order to avoid reaching high values with multiple additions of noise. In other words,

p(x)=k1*exp(−k2x)−k3

for some constants k1, k2 and k3 and with x greater than or equal to 0.

The stored number virtual visits per subject state can be used to remove such when calculating population flows in percentages and the total number of visits.

Addition above is in the general sense of generating a new skew measure based on the skew measure and noise, but actual addition is preferable due to its ease of isolation into a bias term for later exact correction.

Skew measures rendered anonymous by addition of noise may be considered sufficient to provide anonymity without the use of an anonymization module. This is also true even if the noise is only used once as initialization before the data collection. A weakness is that if the anonymized data can be accesses at two points in time, then the number of visits for any specific individual between those moments can trivially be extracted.

Another alternative is to add such noise after every visits. The resulting methods are then more or less equivalent to a noise-masking anonymization module. Note that the method described above of generating a precise correcting bias in the population flow estimate, using the momentary knowledge of the noise, can also be applied to a noise-masking anonymization module and/or hashing module.

In case of continuous skew measures, such as storing precise continuous identifiers, the method may also be used. Such noise in the skew measures may for example be generated based on a sufficient amount of virtual visits for an individual visit to be indistinguishable.

The preferred embodiment for most applications is a combination of methods with an initial anonymizing noisy skew measure with a stored bias correction term generated from the specific noise sample in combination with skew measures generated by a hashing module, for example a group identifier counter. If accuracy of the population flow estimate is more important than anonymity, then relying only on a random initialization of an identifying skew measure may be more appropriate to reduce the variance.

A disadvantage of all noise-based methods is that true noise sources may be scarce and that many sources of pseudorandom noise can be reversed, which would significantly simplify an attack on the anonymization.

On the mechanical level, such anonymized skew measured are generated by the anonymization module, typically online, in part by the received identifier and in part by the identifier skew measure already stored in memory. The noise can be added by the anonymization module and/or by a separate mechanism that adds noise to the memory. Each new identifier skew measure generated based in part on such a noisy identifier skew measure may then be rendered anonymized provided that the noise level is sufficiently high.

In the following, a non-exhaustive number of non-limiting examples will be outlined.

Example—Anonymously Tracking and/or Analysing Flow of Visitors in a Physical or Online Retail Environment Based on Biometric Data

By way of example, there is provided a system, as well as a corresponding method and computer program, for anonymously tracking and/or analysing flow of visitors of a physical or online retail store.

The system is configured to determine, for each retail store visitor in a set or population of multiple visitors, a group identifier based on a hashing function using information representative of an identity of the visitor as input,

-   -   wherein each group identifier corresponds to a group of         visitors, the identity information of which results in the same         group identifier, thereby effectively performing         microaggregation of the set or population of visitors into at         least two groups.

The system is configured to keep track, per group, of visitation data representing the number of visits to two or more tempo-spatial locations by visitors belonging to the group, and the system is also configured to determine at least one flow measure representative of the number of retail store visitors passing from a first tempo-spatial location to a second tempo-spatial location based on visitation data per group identifier.

There is also provided a method, system and corresponding computer program for enabling estimation of a measure of flow or movement of retail store visitors, in a set or population of visitors, between two or more tempo-spatial locations.

In an example, the method comprises the steps of:

-   -   receiving identifying biometric data, wherein the identifying         data includes and/or is based on biometric data, from two or         more retail store visitors;     -   generating, online and by one or more processors, a group         identity for each visitor, (e.g. based on the corresponding         identifying biometric data), that is effectively uncorrelated         with the population flow; and     -   storing: the group identity of each visitor together with data         describing tempo-spatial location; and/or a counter per         tempo-spatial location and group identity.

More generally, the method comprises the steps of:

-   -   receiving identifying data, wherein the identifying data         includes and/or is based on biometric data, from two or more         visitors;     -   generating, online and by one or more processors, an anonymized         identifier for each visitor; and     -   storing: the anonymized identifier of each visitor together with         data representing a subject state; and/or a skew measure of such         an anonymized identifier.

Further, there is provided a method, system and corresponding computer program for generating a measure of flow or movement of retail store visitors between tempo-spatial locations.

In this example, the method comprises the steps of:

-   -   configuring one or more processors to receive counters of         anonymous and approximately independently distributed group         identities based on biometric data originating from visits of         retail store visitors to each of two tempo-spatial locations;     -   generating, using said one or more processors, a population flow         measure between two tempo-spatial locations using a linear         correlation between counters of group identities for each of the         two tempo-spatial locations;     -   storing said population flow measure to a memory.

More generally, the method comprises the steps of:

-   -   configuring one or more processors to receive anonymous         identifier skew measures generated based on biometrically based         identifiers from visits and/or occurrences of visitors to and/or         in each of two tempo-spatial locations or subject states,         wherein each identifier is representative of the identity of an         individual visitor and includes and/or is based on biometric         data;     -   generating, using said one or more processors, a population flow         measure between two tempo-spatial locations or subject states by         comparing the anonymous identifier skew measures between the         tempo-spatial locations or subject states;     -   storing said population flow measure to a memory.

Additional optional aspects as previously described may also be incorporated into this technical solution.

Similar systems and/or methods can for also be used for the purpose to analyze movements or flow in for example smart cities, public events, public transportation, from security surveillance, buildings, airports etc. For example, movement patterns of people can be studied using security cameras and/or specially installed cameras. Such cameras can for example also use infrared, stereovision and other similar technology to improve the biometric measure and/or locate the individual more precisely.

In another example, cameras are used in a retail environment to retrieve images containing facial image data. The location of any face is identified using a face detector neural network. Faces are extracted from the image and a hashing module based on neural networks is applied to create a group identifier per face in the integer range 1-1000. The group identifier is stored together with an anonymized time stamp and a location (e.g. zone 3 in store 2). Optionally additional data, such as activity, is stored together with the location, which then allows statistics not only of location (and time) but also to produce statistics of the series of actions taken by a customer or other similar events and/or circumstances. The correlation between the normalized vectors of group counters at different locations and/or times can be used to measure how visitors move between or within stores, how many customers are returning to the store within various time spans and how exposure to certain visual messages affect the tendency to purchase (e.g. by estimating it using a proxy such as being seen on a camera close to the cash register). Optionally, facial images collected online from viewers of a digital marketing campaign, for example images retrieved from social media profiles, can be converted into anonymous group identifiers and correlated with subsequent visits and/or actions in the store in order to anonymously measure the efficiency of the digital marketing campaign.

Note that biometric data herein refers to data that could theoretically be used to identify people, with high probability, in the general sense, which is a definition which in particular differs from certain legal definitions wherein image data etc is considered to be biometric data solely if it is actually used or intended to be used for identification purposes. For example, a facial image is considered biometric data herein even if it is not intended to be used for identification.

Similar systems could, for example, be used to track people in a smart city, airport, security and/or public transport context.

In another more complex example, data concerning blood pressure is autonomously collected using a wearable device on a monthly basis. The blood pressures are divided into enumerable intervals and self-reported diet compositions are reported using a mobile application and classified into a number of categories. The combination of blood level and diet is used as a subject state. When self-reporting, the subject takes a picture and a facial recognition neural network is used to produce identifying facial recognition feature vectors. The feature vectors are hashed using a decorrelation module consisting of an LSH enumerating a number of localities greater than the population size in order to produce a decorrelated hash with a high probability of reidentification. The identifier of those subjects who have not consented to use of personal data are then anonymized using an anonymization module. The anonymization module then adds an integer drawn from an approximately Gaussian distribution of integer value to this enumeration, with a modulo operation applied if the number is greater than the maximum population, i.e. generating a type of noise-masked identifier. The Gaussian distribution is chosen so that the distributions per original integer are overlapping and identification using the noise-masked identifier unlikely. The noise-masked identifier is stored together with the subject state and descriptions of the camera type and resolution used to take the photo. A vector counting the number of individuals per noise-masked identifier and subject state is used as skew measure. The maximum and minimum correlation, depending on whether the states have independent populations or coinciding, between two states is then estimated using randomly generated feature vectors uniformly distributed in the feature space, which are supplied to a Monte Carlo-estimation that relies on the decorrelation module, the anonymization module, the consent status and a camera-dependent model of the feature vector noise that is relying on the number of various camera types and resolutions. In other words, the Monte Carlo-estimation is used to produce the parameters for a linear transform that generates the population flow estimates when applied to the actual identifiers. These flow estimates are then used to anonymously, for those subjects who have not consented, study the effect of diet on the development of blood pressure by creating a model of how subjects in each combination of diet and blood pressure flow to various states of blood pressure, with diet not used to distinguish states in this second state, in the coming month.

The whole population may also be divided in subpopulations of interest. For example, patients may be divided into subpopulations, for example such as male/female, age, region, etc, before applying the hashing. Each subpopulation is then considered a separate population being studied for the purposes herein, even if the same hashing function may be shared across several subpopulations.

This information can be stored as separate counters, or the additional information can be stored explicitly together with the group identifier.

In each of these examples, multiple visits by the same individual will naively be indistinguishable from multiple visits from different individuals. As such, if the precise number of unique individuals is desired, a behavioural model may, as an example, be combined with the generated measure. We may for example see the correlation over time between some different times to the same location and measure the average number of recurring visits per visitor. Such a behavioural model can then be used, for example, as indicated in the more general description, to compensate the advertising revenue model by dividing the total number of visits by the recurring visits and so generate a measure of the number of unique visitors. Many other types of behavioural model can also be fitted to the data using the general methodology described herein and complex behavioural models may result from the combination of several such submodels.

A particular example of a behavioral model to derive unique visitors may be used to compensate for repeated visits in a short interval being more likely. In these cases, visits from the same group within some time interval might be compensated for or filtered. For example, two visits to the same location within 5 minutes might be considered a single visit or some fractional number, such as 0.01 of a visit, according to some approximation of the probability of these visits being two separate identities.

The whole population may also be divided in subpopulations. For example, visitors may be divided into subpopulations, for example such as male/female, age, region, etc, before applying the hashing. Each subpopulation is then considered a separate population being studied, even if the same hashing function may be shared across several subpopulations. This information can be stored as separate counters, or the additional information can be stored explicitly together with the group identity.

These examples above are not exhaustive of the possibilities.

Examples—Implementation Details

It will be appreciated that the methods and devices described above can be combined and re-arranged in a variety of ways, and that the methods can be performed by one or more suitably programmed or configured digital signal processors and other known electronic circuits (e.g. discrete logic gates interconnected to perform a specialized function, or application-specific integrated circuits).

Many aspects of this invention are described in terms of sequences of actions that can be performed by, for example, elements of a programmable computer system.

The steps, functions, procedures and/or blocks described above may be implemented in hardware using any conventional technology, such as discrete circuit or integrated circuit technology, including both general-purpose electronic circuitry and application-specific circuitry.

Alternatively, at least some of the steps, functions, procedures and/or blocks described above may be implemented in software for execution by a suitable computer or processing device such as a microprocessor, Digital Signal Processor (DSP) and/or any suitable programmable logic device such as a Field Programmable Gate Array (FPGA) device and a Programmable Logic Controller (PLC) device.

It should also be understood that it may be possible to re-use the general processing capabilities of any device in which the invention is implemented. It may also be possible to re-use existing software, e.g. by reprogramming of the existing software or by adding new software components.

It is also possible to provide a solution based on a combination of hardware and software. The actual hardware-software partitioning can be decided by a system designer based on a number of factors including processing speed, cost of implementation and other requirements.

FIG. 11 is a schematic diagram illustrating an example of a computer-implementation 100 according to an embodiment. In this particular example, at least some of the steps, functions, procedures, modules and/or blocks described herein are implemented in a computer program 125; 135, which is loaded into the memory 120 for execution by processing circuitry including one or more processors 110. The processor(s) 110 and memory 120 are interconnected to each other to enable normal software execution. An optional input/output device 140 may also be interconnected to the processor(s) 110 and/or the memory 120 to enable input and/or output of relevant data such as input parameter(s) and/or resulting output parameter(s).

The term ‘processor’ should be interpreted in a general sense as any system or device capable of executing program code or computer program instructions to perform a particular processing, determining or computing task.

The processing circuitry including one or more processors 110 is thus configured to perform, when executing the computer program 125, well-defined processing tasks such as those described herein.

In particular, the proposed technology provides a computer program comprising instructions, which when executed by at least one processor, cause the at least one processor to perform the computer-implemented method described herein. The processing circuitry does not have to be dedicated to only execute the above-described steps, functions, procedure and/or blocks, but may also execute other tasks.

Moreover, this invention can additionally be considered to be embodied entirely within any form of computer-readable storage medium having stored therein an appropriate set of instructions for use by or in connection with an instruction-execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch instructions from a medium and execute the instructions.

The software may be realized as a computer program product, which is normally carried on a non-transitory computer-readable medium, for example a CD, DVD, USB memory, hard drive or any other conventional memory device. The software may thus be loaded into the operating memory of a computer or equivalent processing system for execution by a processor. The computer/processor does not have to be dedicated to only execute the above-described steps, functions, procedure and/or blocks, but may also execute other software tasks.

The flow diagram or diagrams presented herein may be regarded as a computer flow diagram or diagrams, when performed by one or more processors. A corresponding apparatus may be defined as a group of function modules, where each step performed by the processor corresponds to a function module. In this case, the function modules are implemented as a computer program running on the processor.

The computer program residing in memory may thus be organized as appropriate function modules configured to perform, when executed by the processor, at least part of the steps and/or tasks described herein.

Alternatively, it is possible to realize the module(s) predominantly by hardware modules, or alternatively by hardware, with suitable interconnections between relevant modules. Particular examples include one or more suitably configured digital signal processors and other known electronic circuits, e.g. discrete logic gates interconnected to perform a specialized function, and/or Application

Specific Integrated Circuits (ASICs) as previously mentioned. Other examples of usable hardware include input/output (I/O) circuitry and/or circuitry for receiving and/or sending signals. The extent of software versus hardware is purely implementation selection.

It is becoming increasingly popular to provide computing services (hardware and/or software) where the resources are delivered as a service to remote locations over a network. By way of example, this means that functionality, as described herein, can be distributed or re-located to one or more separate physical nodes or servers. The functionality may be re-located or distributed to one or more jointly acting physical and/or virtual machines that can be positioned in separate physical node(s), i.e. in the so-called cloud. This is sometimes also referred to as cloud computing, which is a model for enabling ubiquitous on-demand network access to a pool of configurable computing resources such as networks, servers, storage, applications and general or customized services.

The embodiments described above are to be understood as a few illustrative examples of the present invention. It will be understood by those skilled in the art that various modifications, combinations and changes may be made to the embodiments without departing from the scope of the present invention. In particular, different part solutions in the different embodiments can be combined in other configurations, where technically possible. 

1. A system comprising: one or more processors; an anonymization module configured to, by the one or more processors: receive, for each one of a multitude of individuals comprising individual subjects and/or objects in a population of individuals, identifying information representative of an identity of the individual, wherein the identifying information representative of the identity of the individual includes and/or is based on biometric data, and to generate anonymous identifier skew measures based on identifying information of one or more individuals, wherein anonymization takes place online in real-time and/or near real-time, immediately deleting the identifying information after processing; a memory configured to store at least one anonymous identifier skew measure based on at least one of the generated identifier skew measures; and an estimator configured to, by the one or more processors: receive, from said memory and/or directly from said anonymization module, a number of anonymous identifier skew measures, at least one identifier skew measure for each of at least two subject states of individuals, and to generate one or more population flow measures related to individuals passing from one subject state to another subject state based on the received anonymous identifier skew measures.
 2. The system of claim 1, wherein each identifier skew measure is generated based on two or more identifier density estimates and/or one or more values generated based on identifier density estimates.
 3. The system of claim 1, wherein each identifier skew measure is representing the skew of the identifying information of one or more individuals compared to the expected distribution of such identifying information in the population.
 4. The system of claim 1, wherein the identifier skew measure of the anonymization module is based on a group identifier representing a multitude of individuals.
 5. The system of claim 4, wherein the identifier skew measure is based on a visitation counter.
 6. The system of claim 3, wherein the identifier skew measure is generated based on the identifying information using a hashing function.
 7. The system of claim 6, wherein said one or more population flow measures includes the number and/or ratio of visitors passing from one tempo-spatial location to another tempo-spatial location.
 8. The system of claim 7, wherein at least one of said one or more population flow measures is generated at least partly based on a linear transform of counter information of two or more visitation counters.
 9. The system of claim 8, wherein the anonymization module and/or the identifying information representative of the identity of an individual is stochastic and wherein the stochasticity of the identifying information and/or anonymization module is taken into consideration when generating the linear transform.
 10. The system of claim 1, wherein a baseline corresponding to the expected correlation from two independently generated populations is subtracted when generating the population flow measure(s).
 11. The system of claim 1, wherein each identifier skew measure is generated using a combination of the identifier and noise such that the contribution to the identifier skew measure is rendered anonymous due to a sufficient noise level for a visit to a subject state not being attributable to a specific identifier.
 12. The system of claim 11, wherein the identifier skew measure is based on two or more identifier density estimates.
 13. The system of claim 1, wherein the anonymization module is configured to generate at least one identifier skew measure based on the anonymous identifier skew measure(s) stored in memory, and anonymity is provided by having added sufficient noise to the anonymous identifier skew measure stored in memory, at one or more moments, for the total contribution from any single identifier to be undeterminable.
 14. The system of claim 13, wherein information about the generated noise sample(s) are also stored and used for the lowering the variance in the population flow measure.
 15. The system of claim 1, wherein the identifying information representative of the identity of an individual includes and/or is based on at least one of: iris image, facial image, biometric feature vector and/or body image, fingerprint and/or gait.
 16. The system of claim 1, wherein the subject states include tempo-spatial locations, computer system states in an interaction with the user and/or states of the health and health monitoring of a subject.
 17. The system of claim 1, wherein the subject states are tempo-spatial locations or localities, wherein the anonymization module is configured to generate a group identifier based on the identifying information of the individual to perform microaggregation of the population into corresponding groups, wherein the memory is configured to store visitation counters for each of two or more group identifiers from each of two or more tempo-spatial locations or localities associated with the corresponding individuals, and wherein the estimator is configured to receive counter information from at least two visitation counters, and generate one or more population flow measures related to individuals passing from one tempo-spatial location to another tempo-spatial location.
 18. The system of claim 17, wherein the anonymization module is configured to generate a group identifier based on the identifying information of the individual by using a hashing function.
 19. The system of claim 17, further comprising an input module configured to, by the one or more processors: receive location data, for each one of the multitude of individuals, representative of a tempo-spatial location, and match the tempo-spatial location of the individual with a visitation counter corresponding to the group identifier related to the individual, and each visitation counter for each group identifier also corresponds to a specific tempo-spatial location.
 20. A system for anonymously tracking and/or analyzing flow or movement of individual subjects and/or objects, referred to as individuals, between subject states based on biometric data, wherein the system is configured to determine, for each individual in a population of multiple individuals, an anonymized identifier using identifying information representative of an identity of the individual as input, wherein the identifying information representative of the identity of the individual includes and/or is based on biometric data, wherein each anonymized identifier corresponds to any individual in a group of individuals, the identity information of which results in the same anonymized identifier with probabilities such that no individual generates the anonymized identifier with greater probability than the sum of the probabilities of generating the identifier over all other individuals, wherein anonymization takes place online in real-time and/or near real-time, immediately deleting the identifying information after processing, wherein the system is configured to keep track of skew measures, one skew measure for each of two or more subject states, wherein each skew measure is generated based on anonymized identifiers associated with the corresponding individuals associated with a specific corresponding subject state, and wherein the system is configured to determine at least one population flow measure representative of the number of individuals passing from a first subject state to a second subject state based on the skew measures corresponding to the subject states.
 21. The system of claim 20, wherein the anonymized identifiers are group identifiers and/or noise-masked identifiers.
 22. The system of claim 20, wherein the system is configured to determine, for each individual in a population of multiple individuals, a group identifier based on a hashing function using information representative of an identity of the individual as input, wherein each group identifier corresponds to a group of individuals, the identity information of which results in the same group identifier, thereby performing microaggregation of the population into at least two groups, wherein the subject states are tempo-spatial locations or localities and the skew measures correspond to visitation data, and the system is configured to keep track, per group, of visitation data representing the number of visits to two or more tempo-spatial locations by individuals belonging to the group, and wherein the system is configured to determine at least one population flow measure representative of the number of individuals passing from a first tempo-spatial location to a second tempo-spatial location based on visitation data per group identifier.
 23. The system of claim 20, wherein the system comprises processing circuitry and memory, wherein the memory comprises instructions, which, when executed by the processing circuitry, causes the system to anonymously track and/or analyze flow or movement of individuals.
 24. A surveillance system comprising: the system of claim
 1. 25. A computer-implemented method for enabling anonymous estimation of the amount and/or flow of individual subjects and/or objects, referred to as individuals, in a population moving and/or coinciding between two or more subject states, based on biometric data, said method comprising: receiving identifying data from two or more individuals, wherein the identifying data of each individual includes and/or is based on biometric data; generating, online and by one or more processors, an anonymized identifier for each individual, wherein anonymization takes place online in real-time and/or near real-time, immediately deleting the identifying information after processing; and storing: the anonymized identifier of each individual together with data representing a subject state, and/or a skew measure of such an anonymized identifier.
 26. The method of claim 25, wherein the anonymized identifier is an anonymized identifier skew measure or other anonymized identifier that is effectively uncorrelated with the population flow.
 27. The method of claim 25, wherein the identifying data is correlated in some way with the population flow, and wherein the skew measure is decorrelating and/or the anonymized identifier is generated with a decorrelation module and/or a decorrelating hashing module.
 28. The method of claim 26, wherein the anonymized identifier is an anonymous skew measure and the anonymized skew measure is generated based on a stored anonymous identifier skew measure to which noise has been added at one or more moments.
 29. The method of claim 25, wherein the anonymized identifier is generated by adding noise to the identifying data.
 30. The method of claim 28, wherein a compensation term to be added to a population flow estimate and/or necessary information for generating such a population flow estimate is calculated based on one or more generated noise sample(s) used by the method.
 31. The method of claim 25, wherein any two stored anonymized identifiers or identifier skew measures are not linkable to each other, i.e. there is no pseudonymous identifier linking the states in the stored data.
 32. The method of claim 25, wherein the anonymized identifier is a group identity, and the group identity of each individual is stored together with data representing subject state; and/or a counter per subject state and group identity.
 33. The method of claim 32, wherein the subject state is a tempo-spatial location, a computer system state in an interaction with a user and/or a state of health and/or health monitoring of a subject.
 34. The method of claim 32, wherein activity data representative of one or more actions or activities of each individual is also stored together with the corresponding group identity and data describing subject state.
 35. The method of claim 25, further comprising generating a population flow measure between two subject states.
 36. A computer-implemented method for generating a measure of flow or movement of individual subjects and/or objects, referred to as individuals, between subject states, based on biometric data, said method comprising: configuring one or more processors to receive anonymous identifier skew measures generated online in real-time and/or near real-time, based on biometrically based identifiers from visits and/or occurrences of individuals to and/or in each of two subject states, each identifier being representative of the identity of an individual and including and/or being based on biometric data and being deleted immediately after processing; generating, using said one or more processors, a population flow measure between two subject states by comparing the anonymous identifier skew measures between the subject states; and storing said population flow measure to a memory.
 37. The method of claim 36, wherein the subject states are tempo-spatial locations, computer system states in interaction with a user and/or states of health and/or health monitoring of a subject.
 38. The method of claim 36, wherein the anonymous identifier skew measures are counters of group identities.
 39. The method of claim 36, wherein a single visitor present in one subject state cannot be reidentified in another subject state with high probability using the anonymous identifier skew measures.
 40. The method of claim 36, wherein the generating is not based on data already containing some measure of the population flow between the locations on an individual level and/or microaggregated level.
 41. The method of claim 36, wherein the anonymous identifier skew measures are effectively uncorrelated with the population flow.
 42. The method of claim 36, wherein the population flow estimate is generated based on a linear mapping from the anonymous identifier skew measures.
 43. The method of claim 36, wherein the population flow measure is also generated based on information about noise samples used to anonymize the data.
 44. The method of claim 36, wherein the configuring includes configuring one or more processors to receive counters of anonymous and approximately independently distributed group identities originating from visits of individuals to each of two subject states, and the generating includes generating a population flow measure between two subject states using a linear correlation between counters of group identities for each of the two subject states.
 45. The method of claim 44, wherein the subject states are tempo-spatial locations, and the population flow measure between two tempo-spatial locations is generated using a linear correlation between counters of group identities for each of the two subject states.
 46. The method of claim 25, wherein an anonymous identifier or identifier skew measure for each subject state is based on two or more identifier density estimates.
 47. A non-transitory computer-readable medium having stored thereon a computer program comprising instructions, which when executed by at least one processor, cause the at least one processor to perform the computer-implemented method of claim
 25. 48. (canceled)
 49. A system for performing the method of claim
 25. 